JEE Main Mathematical Reasoning Practice Questions With Solutions

Tell us your JEE Main score & access the list of colleges you may qualify for!

JEE Main Mathematics Mathematical Reasoning Practice Questions

Question 1.

Negation of

p \land (q \land \sim (p \land q))

is :

(\sim (p \land q)) \land q

(\sim (p \land q)) \lor p

p \lor q

\sim (p \lor q)

Question 2.

The statement $(p \land (\sim q)) \lor ((\sim p) \land q) \lor ((\sim p) \land (\sim q))$ is equivalent to _________.

(\sim p) \lor (\sim q)

p \lor (\sim q)

p \lor q

(\sim p) \lor q

Question 3.

The negation of the statement $((A \land (B \lor C)) \Rightarrow (A \lor B)) \Rightarrow A$ is

equivalent to

B \lor \sim C

equivalent to

\sim A

equivalent to

\sim C

a fallacy

Question 4.

Among the two statements

$(S 1) : (p \Rightarrow q) \land (p \land (\sim q))$ is a contradiction and

$(S 2) : (p \land q) \lor ((\sim p) \land q) \lor (p \land (\sim q)) \lor ((\sim p) \land (\sim q))$ is a tautology

both are false.

only (S1) is true.

both are true.

only (S2) is true.

Question 5.

The converse of $((\sim p) \land q) \Rightarrow r$ is

((\sim p) \lor q) \Rightarrow r

(\sim r) \Rightarrow p \land q

(p \lor (\sim q)) \Rightarrow (\sim r)

(\sim r) \Rightarrow ((\sim p) \land q)

Question 6.

The statement $\sim [p \lor (\sim (p \land q))]$ is equivalent to :

(\sim (p \land q)) \land q

\sim (p \lor q)

(p \land q) \land (\sim p)

\sim (p \land q)

Question 7.

The negation of the statement $(p \lor q) \land (q \lor (\sim r))$ is :

((\sim p) \lor r)) \land (\sim q)

(p \lor r) \land (\sim q)

((\sim p) \lor (\sim q)) \lor (\sim r)

((\sim p) \lor (\sim q)) \land (\sim r)

Question 8.

The negation of $(p \land (\sim q)) \lor (\sim p)$ is equivalent to :

p \land q

p \land (\sim q)

p \land (q \land (\sim p))

p \lor (q \lor (\sim p))

Question 9.

Negation of $(p \Rightarrow q) \Rightarrow (q \Rightarrow p)$ is :

(\sim q) \land p

q \land (\sim p)

p \lor (\sim q)

(\sim p) \lor q

Question 10.

Among the statements

(S1) : $(p \Rightarrow q) \lor ((\sim p) \land q)$ is a tautology

(S2) : $(q \Rightarrow p) \Rightarrow ((\sim p) \land q)$ is a contradiction

neither (S1) and (S2) is True

only (S2) is True

both

(S 1)

and

(S 2)

are True

only (S1) is True

Question 1.

Statement $(P \Rightarrow Q) \land (R \Rightarrow Q)$ is logically equivalent to :

(P \Rightarrow R) \land (Q \Rightarrow R)

(P \Rightarrow R) \lor (Q \Rightarrow R)

(P \land R) \Rightarrow Q

(P \lor R) \Rightarrow Q

Question 2.

Which of the following statements is a tautology?

p \lor (p \land q)

(p \land (p \to q)) \to \sim q

p \to (p \land (p \to q))

(p \land q) \to (\sim (p) \to q)

Question 3.

The negation of the expression $q \lor ((\sim q) \land p)$ is equivalent to

(\sim p) \land (\sim q)

(\sim p) \lor q

p \land (\sim q)

(\sim p) \lor (\sim q)

Question 4.

The number of values of

r \in {p, q, \sim p, \sim q}

for which

((p \land q) \Rightarrow (r \lor q)) \land ((p \land r) \Rightarrow q)

is a tautology, is :

Question 5.

$(S 1) (p \Rightarrow q) \lor (p \land (\sim q))$ is a tautology

$(S 2) ((\sim p) \Rightarrow (\sim q)) \land ((\sim p) \lor q)$ is a contradiction.

Then

only (S2) is correct

both (S1) and (S2) are correct

only (S1) is correct

both (S1) and (S2) are wrong

Question 6.

Consider the following statements:

P : I have fever

Q: I will not take medicine

$R$ : I will take rest.

The statement "If I have fever, then I will take medicine and I will take rest" is equivalent to :

((\sim P) \lor \sim Q) \land ((\sim P) \lor \sim R)

(P \lor \sim Q) \land (P \lor \sim R)

((\sim P) \lor \sim Q) \land ((\sim P) \lor R)

(P \lor Q) \land ((\sim P) \lor R)

Question 7.

Among the statements :

$(S 1) ((p \lor q) \Rightarrow r) \Leftrightarrow (p \Rightarrow r)$

$(S 2) ((p \lor q) \Rightarrow r) \Leftrightarrow ((p \Rightarrow r) \lor (q \Rightarrow r))$

only (S1) is a tautology

neither (S1) nor (S2) is a tautology

both (S1) and (S2) are tautologies

only (S2) is a tautology

Question 8.

If $p, q$ and $r$ are three propositions, then which of the following combination of truth values of $p, q$ and $r$ makes the logical expression ${(p \lor q) \land ((\sim p) \lor r)} \to ((\sim q) \lor r)$ false?

p = F, q = T, r = F

p = T, q = T, r = F

p = T, q = F, r = T

p = T, q = F, r = F

Question 9.

Let $Δ, \nabla \in {\land, \lor}$ be such that $(p \to q) Δ (p \nabla q)$ is a tautology. Then

Δ = \lor, \nabla = \lor

Δ = \lor, \nabla = \land

Δ = \land, \nabla = \land

Δ = \land, \nabla = \lor

Question 10.

The statement $(p \land (\sim q)) \Rightarrow (p \Rightarrow (\sim q))$ is

a tautology

equivalent to

(\sim p) \lor (\sim q)

a contradiction

p \lor q

Matrices and Determinants Practice Test Questions with Solutions Attempt Now
3D Geometry Practice Test Questions with Solutions Attempt Now
Definite Integration Practice Test Questions with Solutions Attempt Now
Vector Algebra Practice Test Questions with Solutions Attempt Now
Differential Equations Practice Test Questions with Solutions Attempt Now
Probability Practice Test Questions with Solutions Attempt Now
Limits, Continuity and Differentiability Practice Test Questions with Solutions Attempt Now
Sequences and Series Practice Test Questions with Solutions Attempt Now
Application of Derivatives Practice Test Questions with Solutions Attempt Now
Complex Numbers Practice Test Questions with Solutions Attempt Now
Quadratic Equation and Inequalities Practice Test Questions with Solutions Attempt Now
Binomial Theorem Practice Test Questions with Solutions Attempt Now
Functions Practice Test Questions with Solutions Attempt Now
Circle Practice Test Questions with Solutions Attempt Now
Straight Lines and Pair of Straight Lines Practice Test Questions with Solutions Attempt Now
Inverse Trigonometric Functions Practice Test Questions with Solutions Attempt Now
Parabola Practice Test Questions with Solutions Attempt Now
Permutations and Combinations Practice Test Questions with Solutions Attempt Now
Area Under The Curves Practice Test Questions with Solutions Attempt Now
Statistics Practice Test Questions with Solutions Attempt Now
Ellipse Practice Test Questions with Solutions Attempt Now
Sets and Relations Practice Test Questions with Solutions Attempt Now
Differentiation Practice Test Questions with Solutions Attempt Now
Indefinite Integrals Practice Test Questions with Solutions Attempt Now
Trigonometric Ratio and Identites Practice Test Questions with Solutions Attempt Now
Trigonometric Equations Practice Test Questions with Solutions Attempt Now
Height and Distance Practice Test Questions with Solutions Attempt Now
Hyperbola Practice Test Questions with Solutions Attempt Now
Properties of Triangle Practice Test Questions with Solutions Attempt Now

Unlock Your Results: Answer Key Available for Download

Still have questions about JEE Main ? Ask us.

Typical response between 24-48 hours
Get personalized response
Free of Cost
Access to community

JEE Main Mathematical Reasoning Practice Questions With Solutions

JEE Main Mathematics Mathematical Reasoning Practice Questions

Question 1.

Question 2.

Question 3.

Question 4.

Question 5.

Question 6.

Question 7.

Question 8.

Question 9.

Question 10.

Question 1.

Question 2.

Question 3.

Question 4.

Question 5.

Question 6.

Question 7.

Question 8.

Question 9.

Question 10.

Other Topics of that Section

Quick Links

Still have questions about JEE Main ? Ask us.

Related News

Related Articles

Popular Degrees

Popular Specializations

Engineering Colleges in States

Engineering Colleges in Cities

Popular Engineering Exams

Engineering Colleges by College Type